Schnatter said: "By not resolving the current debacle to the players' and owners' satisfaction, NFL leadership has hurt Papa John's shareholders. ... This should have been nipped in the bud a year and a half ago."

Papa John's has been one of the most-recognized NFL partners for two years straight. Papa John's execs said when the NFL's image is hurt, so is the company's.

NFL TV ratings are down this year. But some analysts and media executives say an overabundance of games throughout the week are swaying the numbers — instead of a sign sports fans are boycotting over protests during the anthem.

Correction: A previous version of this article was not clear in its discussion of the NFL protests. The players are kneeling to protest social injustices, not the national anthem itself.